Published version (c)2006 Optical Society of America. This paper was published in Applied Optics and can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-11-1753

The electro-optic effect between an ultrafast optical probe pulse and an ultrashort terahertz pulse is shown to depend on the time derivatives of the product of the probe and the terahertz electric fields. Application of this theory to temporally resolved single-shot terahertz detection techniques, where the electro-optic effect is temporally localized within an optical probe pulse, shows that the description presented here differs fundamentally and verifiably from that commonly used in literature.